Equivariant holomorphic differential operators and finite averages of values of L-functions

Using pullback formulas for both Siegel-Eisenstein series and Jacobi-Eisenstein series the second author obtained relations between critical values of certain L-functions. To extend these relations to other critical values we use holomorphic differential operators for both types of pullbacks. The differential operators in question are well known in the Siegel case whereas for the Jacobi case they have to be developed from scratch. To compare the two pullbacks, we have furthermore to establish a relation of unexpected nature between the two types of differential operators.